A pipe has a porous section of length L as shown in the figure. Velocity at the start of this section of V0. If fluid leaks into the pipe through the porous section at a volumetric rate per unit area q(x/L)2, what will be axial velocity in the pipe at any „x‟? Assume incompressible one dimensional flow i.e., no gradients in the radial direction ?

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A pipe has a porous section of length L as shown in the figure. Velocity at the start of this section of V0. If fluid leaks into the pipe through the porous section at a volumetric rate per unit area q(x/L)2, what will be axial velocity in the pipe at any „x‟? Assume incompressible one dimensional flow i.e., no gradients in the radial direction ?

A. VX = V0 + q (x3/L2D)
B. VX = V0 + ⅓q (x3/L2)
C. VX = V0 + 2q (x2/LD)
D. VX = V0 + (4/3) q (x3/L2D)